The Lyalpha emission line has been proven to be a powerful tool for studying evolving galaxies at the highest redshift. However, in order to use Lyalpha as a physical probe of galaxies, it becomes vital to know the Lyalpha escape fraction (f Lyalpha esc). Unfortunately, due to the resonant nature of Lyalpha, f Lyalpha esc may vary unpredictably and requires empirical measurement. Here, we compile Lyalpha luminosity functions (LFs) between redshifts z = 0 and 8 and, combined with Halpha and ultraviolet data, assess how f Lyalpha esc evolves with redshift. We find a strong upward evolution in f Lyalpha esc over the range z = 0.3-6, which is well fit by the power law f Lyalpha escvprop(1 + z)xiwith xi = (2.57+0.19 -0.12). This predicts that f Lyalpha esc should reach unity at z = 11.1. By comparing f Lyalpha esc and E B-V in individual galaxies we derive an empirical relationship between f Lyalpha esc and E B-V , which includes resonance scattering and can explain the redshift evolution of f Lyalpha esc between z = 0 and 6 purely as a function of the evolution in the dust content of galaxies. Beyond z ≈ 6.5, f Lyalpha esc drops more substantially, an effect attributed to either ionizing photon leakage, or an increase in the neutral gas fraction of the intergalactic medium. While distinguishing between these two scenarios may be extremely challenging, by framing the problem this way we remove the uncertainty of the halo mass from Lyalpha-based tests of reionization. We finally derive a new method by which to estimate the dust content of galaxies, based purely upon the observed Lyalpha and UV LFs. These data are characterized by an exponential with an e-folding scale of z EBV ≈ 3.4.